This paper presents an approach to optimal design of elastic flywheels using an Injection Island Genetic Algorithm (iiGA), summarizing a sequence of results reported in earlier publications. An iiGA in combination with a structural finite element code is used to search for shape variations and material placement to optimize the Specific Energy Density (SED, rotational energy per unit weight) of elastic flywheels while controlling the failure angular velocity. iiGAs seek solutions simultaneously at different levels of refinement of the problem representation (and correspondingly different definitions of the fitness function) in separate subpopulations (islands). Solutions are sought first at low levels of refinement with an axi-symmetric plane stress finite element code for high-speed exploration of the coarse design space. Next, individuals are injected into populations with a higher level of resolution that use an axi-symmetric three-dimensional finite element code to “fine-tune” the structures. A greatly simplified design space (containing two million possible solutions) was enumerated for comparison with various approaches that include: simple GAs, threshold accepting (TA), iiGAs and hybrid iiGAs. For all approaches compared for this simplified problem, all variations of the iiGA were found to be the most efficient. This paper will summarize results obtained studying a constrained optimization problem with a huge design space approached with parallel GAs that had various topological structures and several different types of iiGA, to compare efficiency. For this problem, all variations of the iiGA were found to be extremely efficient in terms of computational time required to final solution of similar fitness when compared to the parallel GAs.